What is Rhythm?

Rhythm is the (repetitive) timing framework of music. When you read about rhythm (see Whiteside), it often seems like a mysterious aspect of music that only "inborn talent" can express. Or perhaps you need to practice it all your life, like drummers. Most frequently, however, correct rhythm is simply a matter of accurate counting, of correctly reading the music, especially the time signatures. This is not as easy as it sounds; difficulties often arise because most indications for rhythm are not explicitly spelled out everywhere on the music score since it is part of things like the time signature that appears only once at the beginning (there are too many such "things" to be listed here, such as the difference between a waltz and a mazurka). In many instances, the music is created mainly by manipulating these rhythmic variations so that rhythm is one of the most important elements of music. In short, most rhythmic difficulties arise from not reading the music correctly. This often happens when you try to read the music HT; there is just too much information for the brain to process and it can't be bothered with rhythm, especially if the music involves new technical skills. That initial reading mistake then becomes incorporated into the final music that you practice.
Definition of Rhythm: Rhythm consists of 2 parts: timing and accents, and they come in 2 forms, formal and logical. The mysteries surrounding rhythm and the difficulties encountered in defining rhythm arise mainly from the "logical" part, which is at once the key element and the most elusive. So let's tackle the simpler formal rhythms first. Just because they are simpler does not mean that they aren't important; too many students make mistakes with these elements which generally renders the music unrecognizable in terms of what it should sound like.
Formal Timing: The formal timing rhythm has a name, "Time Signature", and is indicated at the very beginning of any music score. The major time signatures are waltz (3/4), common time (4/4), "cut time" (2/2), and 2/4. The waltz has 3 beats per bar (measure), etc.; the number of beats per bar is indicated by the numerator. 4/4 is the most common and is often not even indicated, although it should be indicated by a "C" at the beginning (you can remember it as "C stands for common"). Cut time is indicated by the same "C", but with a vertical line down the center (cuts the "C" in half). The reference note is indicated by the denominator, so that the 3/4 waltz has 3 quarter-notes per bar, and 2/4 is, in principle, twice as fast as 2/2 cut time.
Formal Accents: Each time signature has its own formal accent (louder or softer beats). If we use the convention that 1 is the loudest, 2 is softer, etc., then the waltz has the formal accent 133 (the famous oom-pha-pha); the first beat gets the accent. Common time has the formal accent 1323, and cut time and 2/4 have the accent 12. The Mazurka has the accent 331, and a syncopation is a rhythm in which the accent is placed at an arbitrary (but fixed) location within a bar; for example a syncopated 4/4 might be 2313 or 2331. Note that the 2331 rhythm is fixed throughout the composition, but the 1 is at a non-conventional location.
Logical Timing and Accents: This is where the composer injects his music. It is a change in timing and loudness from the formal rhythm. Although rhythmic logic is not necessary, it is almost always there. Well known components of timing rhythmic logic are accel. (to make things more exciting), decel. (perhaps to indicate an ending) or rubato. Examples of dynamic rhythmic logic are increasing or decreasing loudness, forte, PP, etc.
An interesting composition in which the formal and logical rhythms can be discerned fairly easily is Beethoven's Tempest Sonata (Op. 31, #2), especially in the 3rd movement. For example, in the 3rd movement, the first 3 bars are 3 repetitions of the same structure, and they simply follow the formal rhythm. However, in bars 43-46, there are 6 repetitions of the same structure in the RH, but they must be squeezed into 4 formal rhythmic bars! If you make 6 identical repetitions in the RH, you are wrong! In addition, in bar 47, there is an unexpected "sf" that has nothing to do with the formal rhythm, but is an absolutely essential logical rhythm.
If rhythm is so important, what guidance can one use, in order to cultivate it? Obviously, you must treat rhythm as a separate subject of practice for which you need a specific program of attack. Therefore, during the initial learning of a new piece, set aside some time for working on the rhythm. A metronome, especially one with advanced features, can be helpful here. First, you must double check that your rhythm is consistent with the time signature. This can't be done in your mind even after you can play the piece -- you must revisit the sheet music and check every note. Too many students just play a piece a certain way "because it sounds right"; you can't do that. You must check with the score to see if the correct notes carry the correct accent strictly according to the time signature. Only then, can you decide which rhythmic interpretation is the best way to play and where the composer has inserted violations of the basic rules (very rare); more often the rhythm indicated by the time signature is strictly correct but sounds counter-intuitive. An example of this is the mysterious "arpeggio" at the beginning of Beethoven's Appassionata (Op. 57). A normal arpeggio (such as CEG) would start with the first note (C), which should carry the accent (downbeat). However, Beethoven starts each bar at the third note of the arpeggio (the first bar is incomplete and carries the first two notes of the "arpeggio"); this forces you to accent the third note, not the first note, if you follow the time signature correctly. We find out the reason for this odd "arpeggio" when the main theme is introduced in bar 35. Note that this "arpeggio" is just an inverted, schematized (simplified) form of this theme. Beethoven had psychologically prepared us for the main theme by giving us only the rhythm! This is why he repeats it, after raising it by a curious interval -- he just wanted to make sure that we recognized the unusual rhythm (he used the same device at the beginning of his 5th symphony, where he repeated the 4-note motif at a lower pitch). Another example is Chopin's Fantaisie-Impromptu. The first note of the RH (bar 5) must be softer than the second. Can you find at least one reason why? Although this piece is in double time, it may be instructive to practice the RH as 4/4 to make sure that the wrong notes are not emphasized.
Check the rhythm carefully when you start HS. Then check again when you start HT. When the rhythm is wrong, the music usually becomes impossible to play at speed. Thus, if you have unusual difficulty in getting up to speed, it is a good idea to check the rhythm. In fact, incorrect rhythmic interpretation is one of the most common causes of speed walls and why you have trouble HT. When you make an rhythmic error, no amount of practice will enable you to get up to speed! This is one of the reasons why outlining works: it simplifies the job of correctly reading the rhythm. Conversely, when outlining, concentrate on rhythm. Also, when you first start HT, you may have more success by exaggerating the rhythm. Rhythm is another reason why you should not attempt pieces that are too difficult for you. If you don't have sufficient technique, you will not be able to control the rhythm. What can happen is that the lack of technique will impose an incorrect rhythm into your playing, thus creating a speed wall.
Next, look for the special rhythmic markings, such as "sf" or accent marks. Finally, there are situations in which there are no indications on the music and you simply have to know what to do, or listen to a recording in order to pick up special rhythmic variations. Therefore, as part of your practice routine, you should experiment with rhythm, accenting unexpected notes, etc., so see what might happen.
Rhythm is also intimately associated with speed. This is why you need to play most Beethoven compositions above certain speeds; otherwise, the emotions associated with the rhythm and even the melodic lines can be lost. Beethoven was a master of rhythm; thus you cannot play Beethoven successfully without paying special attention to rhythm. He usually gives you at least two things simultaneously: (i) an easy-to-follow melody that the audience hears, and (ii) a rhythmic device that controls what the audience feels. Thus in the first movement of his Pathetique (Op. 13), the agitated LH tremolo controls the emotions while the audience is preoccupied with listening to the curious RH. Therefore a mere technical ability to handle the fast LH tremolo is insufficient -- you must be able to control the emotional content with this tremolo. Once you understand and can execute the rhythmic concept, it becomes much easier to bring out the musical content of the entire movement, and the stark contrast with the Grave section becomes obvious.
There is one class of rhythmic difficulties that can be solved using a simple trick. This is the class of complex rhythms with missing notes. A good example of this can be found in the 2nd movement of Beethoven's Pathetique. The 2/4 time signature is easy to play in bars 17 to 21 because of the repeated chords of the LH that maintain the rhythm. However, in bar 22, the most important accented notes of the LH are missing, making it difficult to pick up the somewhat complex play in the RH. The solution to this problem is to simply fill in the missing notes of the LH! In this way, you can easily practice the correct rhythm in the RH.
In summary, the "secret" of great rhythm is no secret -- it must start with correct counting (which, I must re-emphasize, is not easy). For advanced pianists, it is of course much more; it is magic. It is what distinguishes the great from the ordinary. It is not just counting the accents in each bar but how the bars connect to create the developing musical idea. For example, in Beethoven's Moonlight (Op. 27), the beginning of the 3rd movement is basically the 1st movement played at a crazy speed. This knowledge tells us how to play the 1st movement, because it means that the series of triplets in the 1st movement must be connected in such a way that they lead to the culmination with the three repeated notes. If you simply played the repeated notes independently of the preceding triplets, they will lose their real impact. Rhythm is also that odd or unexpected accent that our brains somehow recognize as special. Clearly, rhythm is a critical element of music to which we must pay special attention.